Diagonals of a Rectangle are Congruent

Q.

A diagonal of a rectangle is inclined to one side of the rectangle at ${25}^{\circ }$. Find acute angle between the diagonals.

1. ${55}^{\circ }$

2. ${50}^{\circ }$

3. ${60}^{\circ }$

4. ${65}^{\circ }$

Q. Quadrilateral EFGH is a rectangle in which J is the point of intersection of the diagonals. If JF = $8x+4$ and EG = $24x–8$, find the value of $x$.

1. 1.5
2. 2
3. 3
4. 4

Q.

The diagonals of a rectangle are equal.

1. True

2. False

Q. Question 152 (i)
A rectangle MORE is shown below.

Answer the following questions by giving an appropriate reason.
Is RE = OM?

Q.

Prove that the diagonals of a rectangle are equal. [3 MARKS]

Q.

ABCD is a rectangle. If OB = $x+2$ and AC = $5x-2$, then find the measure of AC.

1. 7 units
2. 8 units
3. 6 units
4. 9 units

Q. It is possible to construct a rectangle ABCD with $AC=8cm$ and $BD=6cm$

1. False
2. True

Q. If the diagonals of a parallelogram are equal and don't intersect at right angles, then it is called a.

1. rhombus
2. rectangle
3. kite
4. Square

Q.

The possible number of diagonals of the following figure are

1. 2

2. 5

3. 3

4. 4

Q.

ABCD is a rectangle. If OB = x + 2 and AC = 5x - 2, then find the measure of AC.

1. 6 units

2. 7 units

3. 8 units

4. 9 units

Q. In the given figure, PQRS is a rectangle if $\angle RPQ={30}^{\circ }$. Then, the value of (x + y) is:

1. ${90}^{\circ }$

2. ${150}^{\circ }$

3. ${120}^{\circ }$

4. ${180}^{\circ }$

Q. State True or False In the given fig. $ABP$ is a straight line $BD\parallel PC$, then the quadrilateral ABCD is equal in area to $\Delta APD$

1. True
2. False